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Families of "asymptotically regular" LDPC block code ensembles can be formed by terminating (J,K)-regular protograph-based LDPC convolutional codes. By varying the termination length, we obtain a large selection of LDPC block code ensembles…
Decoding algorithms based on approximate tensor network contraction have proven tremendously successful in decoding 2D local quantum codes such as surface/toric codes and color codes, effectively achieving optimal decoding accuracy. In this…
We discuss the performance of Low-Density-Parity-Check (LDPC) codes decoded by means of Linear Programming (LP) at moderate and large Signal-to-Noise-Ratios (SNR). Utilizing a combination of the previously introduced pseudo-codeword-search…
We initiate the probabilistic analysis of linear programming (LP) decoding of low-density parity-check (LDPC) codes. Specifically, we show that for a random LDPC code ensemble, the linear programming decoder of Feldman et al. succeeds in…
We study the problem of covering a given set of $n$ points in a high, $d$-dimensional space by the minimum enclosing polytope of a given arbitrary shape. We present algorithms that work for a large family of shapes, provided either only…
Reed-Muller (RM) codes are known for their good maximum likelihood (ML) performance in the short block-length regime. Despite being one of the oldest classes of channel codes, finding a low complexity soft-input decoding scheme is still an…
Constructing quantum LDPC codes with a minimum distance that grows faster than a square root of the length has been a major challenge of the field. With this challenge in mind, we investigate constructions that come from high-dimensional…
In this paper, we propose a policy-guided Monte Carlo Tree Search (MCTS) decoder that achieves near maximum-likelihood decoding (MLD) performance for short block codes. The MCTS decoder searches for test error patterns (TEPs) in the…
A new protograph-based framework for message passing (MP) decoding of low density parity-check (LDPC) codes with Hamming weight amplifiers (HWAs), which are used e.g. in the NIST post-quantum crypto candidate LEDAcrypt, is proposed. The…
We investigate random spatially coupled low-density parity-check (SC-LDPC) code ensembles over finite fields. Under different variable-node edge-spreading rules, the random Tanner graphs of several coupled ensembles are defined by multiple…
This paper analyzes the distribution of cycle lengths in turbo decoding and low-density parity check (LDPC) graphs. The properties of such cycles are of significant interest in the context of iterative decoding algorithms which are based on…
A low-density parity-check (LDPC) code is a linear block code described by a sparse parity-check matrix, which can be efficiently represented by a bipartite Tanner graph. The standard iterative decoding algorithm, known as belief…
We propose a decoder for quantum low density parity check (LDPC) codes based on a beam search heuristic guided by belief propagation (BP). Our beam search decoder applies to all quantum LDPC codes and achieves different speed-accuracy…
We study tensor completion (TC) through the lens of low-rank tensor decomposition (TD). Many TD algorithms use fast alternating minimization methods to solve highly structured linear regression problems at each step (e.g., for CP, Tucker,…
In this paper, we introduce low-complexity multidimensional discrete cosine transform (DCT) approximations. Three dimensional DCT (3D DCT) approximations are formalized in terms of high-order tensor theory. The formulation is extended to…
The speed at which two remote parties can exchange secret keys over a fixed-length fiber-optic cable in continuous-variable quantum key distribution (CV-QKD) is currently limited by the computational complexity of post-processing algorithms…
Recent developments have shown the existence of quantum low-density parity check (qLDPC) codes with constant rate and linear distance. A natural question concerns the efficient decodability of these codes. In this paper, we present a linear…
Pre-transformed polar codes (PTPCs) form a class of codes that perform close to the finite-length capacity bounds. The minimum distance and the number of minimum weight codewords are two decisive properties for their performance. In this…
In this paper a new class of lattices called turbo lattices is introduced and established. We use the lattice Construction D to produce turbo lattices. This method needs a set of nested linear codes as its underlying structure. We benefit…
We consider linear-programming (LP) decoding of low-density parity-check (LDPC) codes. While it is clear that one can use any general-purpose LP solver to solve the LP that appears in the decoding problem, we argue in this paper that the LP…